Ch. 4 Physical Principles of CT

Transcription

1 Ch. 4 Physical Principles of CT CLRS 408: Intro to CT Department of Radiation Sciences Review: Why CT? Solution for radiography/tomography limitations Superimposition of structures Distinguishing between structures with similar densities Used in radiation therapy planning instead of traditional fluoroscopy Used to show anatomy with NM functional imaging and for attenuation correction in fusion studies Review: Why CT? Eliminates superimposition Improves image contrast (reduces scatter) Detects small differences in tissue contrast Shows cross-sectional anatomy are subject to digital post-processing to produce 3D images 1

2 CT Process Beam of well-collimated x-rays transmitted thru cross-section of pt Beam geometry = size & shape of beam emanating from x-ray tube and passing thru pt to strike a set of detectors that collects radiation Attenuation data CT Process Transmitted radiation strikes detectors that can measure small differences Data received from detectors processed by digital computer * To produce a CT image 1. Systematically collect transmission values and send to computer 2. Determine linear attenuation coefficients (µ) 3. Convert µ to CT number for each pixel 4. Assign gray level to pixel, according to CT # I = I o e -µx 2

3 Physical Principles (i.e. physics & math) 1. Data Acquisition 2. Image Data Processing 3. Display / store / communicate the results Physical Principles: 1) Data Acquisition Systematic collection of information to produce the CT image 1. Slice-by-slice (Image A) 2. Volume acquisition (Image B) Image A Image B Data Acquisition Slice-by-slice Data collected thru different beam geometries Steps: X-ray tube rotates around pt Collects data from 1 st slice Tube stops Pt moves Next slice is scanned Repeated until entire area of interest is scanned 3

4 Data Acquisition Volume acquisition Data collected thru spiral/helical CT geometry Single-slice spiral/helical CT (SSCT): X-ray tube rotates around pt Traces spiral/helical path to scan entire volume of tissue Patient holds a single breath Multi-slice spiral/helical CT (MSCT) Improve the volume coverage speed performance Generate multiple slices per one revolution of x-ray tube Data Acquisition 1 st step: Scanning X-ray tube and detectors rotate around pt to collect views Detectors measure the radiation transmitted thru patient from various locations Relative transmission values= intensity at source (I O ) log( ) intensity at detector (I) Physical Principles: 2) Determine Attenuation Coefficients Attenuation: reduction in intensity of beam as it passes through an object CT reconstruction is based on attenuation of the structures in the path of the beam computer 4

5 Attenuation in CT In homogeneous beam all photons have the same energy A.K.A. monochromatic or monoenergetic beam Hounsfield used in initial experiments Homogenous beam (monochromatic / monoenergetic) Attenuation in CT In a heterogeneous beam photons have different energies A.K.A. polychromatic beam Modern CT Heterogenous beam (polychromatic) Attenuation in CT Because CT has heterogeneous beam: 1. Effective atomic density (# of atoms/volume) 2. Atomic number (lead, copper, calcium) 3. Radiation photon energy of beam low energy high energy This differential attenuation of body tissues produces the various shades of gray in a diagnostic image 5

6 What is a linear attenuation coefficient (µ)? Quantitative measurement indicating amount of attenuation that has occurred with unit of per centimeter (linear) Degree of attenuation for each voxel determined by the CT computer Result of absorption and scattering X-rays can be attenuated photoelectric effect X-Rays can be attenuated and scattered by the Compton effect * CT & Energy Dependence Attenuation (µ t ) is dependent on energy of x-ray beam The higher the energy of the beam, the less the µ t CT uses high kv technique ( ) Reduces dependence of µ on photon energy Reduces contrast at bone/soft tissue Produces high # of photons reaching detector (flux) DSCT uses high and low kv sources Images from KJR Lambert-Beer Law Describes what happens to photons as they travel through the tissues Based on homogenous beam I = I o e -µx 6

7 I = I o e -µx I - transmitted intensity (what reaches detector) I o - original intensity (what leaves tube) e - Euler s constant/base of natural logarithm (2.718) µ - linear attenuation coefficient x - thickness of object We know I, I o, e and x So we (the computer!) can solve for µ Lambert-Beer Law True for homogeneous = intensity or kv does not change Necessary to make heterogeneous beam in CT approximate a homogeneous beam to satisfy the equation Formula is modified to measure number (N) of photons that exit the tissue instead of intensity (I) N = N o e -µx *** we still use this formula to determine µ THIS is more realistic! Instead of determining one µ for radiation passing through pt, it is subdivided to provide calculated µ s for many segments along the path: N = N o e - µx N 0 µ 1 µ 2 µ 3 µ 4 µ 5 µ 6 µ 7 µ 8 µ 9 µ 10 N N = N 0 e -(µ 1 + µ 2 + µ 3 + µ 4 + µ 5 + µ 6 + µ 10 ) x 7

8 Physical Principles: 3) Convert to CT Numbers A.K.A. Hounsfield Unit Each pixel in reconstructed image is assigned a CT number, based on attenuation coefficient (µ) CT number related to µ of water: µ t -µ w CT# = µ w K µ t = µ of tissue µ w = µ of water K = scaling factor CT Numbers µ CT # = t -µ w µ w K 1000 CT numbers form a scale Hounsfield scale has K = CT number of water is 0 Scanners are calibrated so CT number of water is always valued at 0 water air bone CT Numbers Shades of gray are assigned to CT Numbers Baseline is water assigned value of 0 Cortical bone is most dense values to Air is least dense values to Every shade of gray in between is assigned a unique CT Number 8

9 Examples of CT Numbers Examples of CT Numbers Calculating CT # s If µ bone = 0.38, µ water = 0.19, µ air = 0 µ CT# = t -µ µ w w K CT # of bone = x 1000 = CT # of water = x 1000 = CT # of air = 9

10 Calculating CT # s If µ bone = 0.38, µ water = 0.19, µ air = 0 µ CT# = t -µ µ w w K CT # of bone = x 1000 = CT # of water = x = 0 CT # of air = x 1000 = Physical Principles: 4) Image Display bone 0 water air Image Data Processing Raw data data received from the detectors Undergo preprocessing corrections made and reformatting of the data occurs Scan data represent attenuation readings Converted into digital image characterized by CT # Accomplished by mathematical procedures reconstruction algorithms Reconstructed image Displayed for viewing and sent for storage/pacs 10

11 Image Display and Manipulation Display resolution Windowing Image format FOV Matrix size Pixel size Bit depth Display (Monitor) Resolution Related to size of matrix # of rows and columns the monitor can display 64 x x x 2048 We already know how to calculate the # of pixels in each matrix. Windowing Image includes range of CT # s to 1000 (or some variation) Can adjust window width and window level of image to display different gray scale values for different tissue types Appears white Appears black 11

12 Window Width (WW) Range of CT #s that are displayed as shades of gray CT# as a group Long scale / low contrast Controls displayed image contrast Window Level (WL) Determines CT # that will be the center of WW Controls image brightness Determined by tissue density that occurs most frequently within an anatomic structure WW and WL Top: 1000 Top: 0 Bottom: Bottom: Appears white Top: 500 Bottom: -500 WW = 2000 WW = 1000 WL = 0 WL = WW = 1000 WL = Appears black 12

13 Windowing Pixel Size Related to FOV and matrix size Pixel size (mm) = FOV (mm) matrix size Calculate pixel size: FOV = 20 cm and matrix size is 256 x 256 Pixel size (mm) = 200 mm 256 mm =.78 mm We know this already! Voxel Volume Voxel 3 dimensional height, width, depth Calculated by multiplying pixel dimensions by the slice thickness Pixel =.5 mm by.5 mm; slice thickness = 3 mm: Voxel volume =.5 x.5 x 3 =.75 mm 3 13

14 Technological Considerations Ultimate goal produce high-quality CT images with minimal radiation Does it work quickly/efficiently? Are the images high quality? Is the patient comfortable? Is minimal radiation dose used? Data Flow in CT Advantages of CT 1. Excellent low-contrast resolution Highly collimated beam used to take images of a cross-sectional slice of the patient More sensitive radiation detectors are used to measure the radiation transmitted through the slice CT offers best low contrast resolution compared with radiography, nuclear medicine, and ultrasonography, but not MRI 2. Image manipulation (WW/WL) Contrast scale can be varied to suit the needs of the observer 3. Single breath hold, faster processing Volume data acquisition in single breath rather than slice-by-slice Improvements in 3D imaging, multiplanar image reformation, and other applications 14

15 Advantages of CT 4. Newer techniques/procedures Quantitative CT, High spatial resolution CT, SPECT/CT, PET/CT, Perfusion CT, Dynamic CT, CT simulation for radiation therapy treatment planning, etc 5. Digital manipulation/reconstruction With image processing algorithms, image can be modified to enhance its information content or analyzed to obtain information about shape / texture of lesions 6. 3D Imaging Imaging intended to enhance image information content Improve diagnostic interpretation skills of the radiologist Limitations of CT 1. Less detailed spatial resolution in lp/mm compared with radiography 2. Increased radiation dose for similar anatomy 3. Some anatomy still difficult to image Soft tissues are surrounded by large amounts of bone (posterior fossa, spinal cord, pituitary, interpetrous space) causing artifacts 4. Artifacts Metallic objects on/in pt produces streak artifacts on CT images Also creates other artifacts not common to radiography 5. Limited in slice orientation The End 15